Preheat the oven to 400 F. In a large saute pan set on medium-high heat, melt the butter. Add the sugar and stir for 3 minutes with a wooden spoon until the sugar mixture is a golden caramel brown color, but still somewhat grainy in texture. Add the apple slices, stirring well to coat each slice. Reduce the heat to medium and cook for 10 minutes, uncovered, stirring often. Cover and cook 10 minutes longer. Remove from the heat and let cool slightly.

Roll the sheet of puff pastry out until it's large enough to cut a 10 inch circle. Arrange part of the apples slices in a decorative circular pattern in the bottom of a 9 inch pie pan. When you eventually serve this "upside-down", this will be the top of the tart, so make this as pretty as possible. (If the saute pan in which the apples were cooked is ovenproof, it is not necessary to transfer them to a pie pan.) Pile the remaining slices on top along with any of the juices remaining in the pan. Place the circle of puff pastry over the apples and tuck the excess dough down inside the pan.

Bake for 12 minutes, until the pastry is golden brown, puffed and crispy. Using oven mitts, carefully invert the pie into a large serving plate. The caramel sauce is very hot, so be careful not to get it on yourself.